Enhancement: Add PWA support (Progressive Web App)

**Description:**
Make the app installable as a PWA:

- Add `public/manifest.json` with app name, icons, theme color
- Add service worker via `next-pwa` or manual implementation
- Cache static assets
- Add `<link rel="manifest">` in `layout.tsx`
- Add Apple touch icon

**Acceptance Criteria:**
- App is installable on mobile
- Lighthouse PWA score ≥ 80

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